Geospatial/SAE workshop

Vector files (shapefiles)

Josh Merfeld

November 2025

Getting started with geospatial data

  • What are we doing today?
    • Shapefiles
      • Polygons
      • Points
      • Lines
      • Mapping with the package sf
    • Coordinate reference systems
      • Latitude/longitude
      • Projections

Shapefiles

  • Shapefiles are a common format for geospatial data
    • They are a form of vector data
  • Shapefiles are made up of at least three files:
    • .shp - the shape itself
    • .shx - the index
    • .dbf - the attributes
    • .prj - the projection
      • This one is not technically necessary! But it’s common to have.
    • What these all mean isn’t important for now, just make sure they are there! Check the week2files folder on github.

Let’s look at Northern Malawi

  • Collection of features

  • One feature

Types of features

  • Polygons
    • Areas
    • Districts, countries, etc.
  • Lines
    • Lines
    • Roads, rivers, etc.
  • Points
    • Points

Let’s start with polygons

Imagine a rectangle, on a coordinate plane

Imagine a rectangle, on a coordinate plane

Imagine a rectangle, on a coordinate plane

  • We need four points.
  • But polygons in shapefiles are a little different.
    • We have to “close” the feature so it knows it’s a polygon!
  • We do this by adding a fifth point: the same as the first point!
Five points (vertices) in our feature
X value Y value
Point 1 1 1
Point 2 3 1
Point 3 3 3
Point 4 1 3
Point 5 1 1

All features are made of vertices

  • So we have all our vertices (489 of them!)
  • The question:
    • What is the coordinate system here?

All features are made of vertices

  • So we have all our vertices (489 of them!)
  • The question:
    • What is the coordinate system here?
  • We will return to this in a bit!

One more example of polygons

One more example of polygons

Lines

  • Lines are also made up of vertices
  • But they are not closed

Lines example - “Primary” roads in India (2014)

One road




Length of this line feature: 1619.93 (m)


Points

  • Points are exactly what they sound like: points!

  • What could be a point?

Points

  • Points are exactly what they sound like: points!

  • What could be a point?

    • A city
    • A weather station
    • A tree
    • A household
    • etc.

What do you think this is?

What do you think this is?

Train stations! First 15

name name_en railway geometry
지평 |J pyeong | tation | OINT (127.6291 37.47681) |
국수 |G ksu | tation | OINT (127.3993 37.51617) |
양평 |Y ngpyeong | tation | OINT (127.4919 37.49285) |
공릉 |G ngneung | tation | OINT (127.073 37.62564) |
남광주 |Na gwangju | s ation | P INT (126.9228 35.13944) |
공항 |A rport | tation | OINT (126.8117 35.1441) |
농성 |N ngseong | tation | OINT (126.884 35.15322) |
금남로5가 |Geu namro 5-ga | st tion | PO NT (126.9101 35.15371) |
금남로4가 |Geu namno 4(sa)-ga | st tion | PO NT (126.9146 35.15071) |
소태 |S tae | tation | OINT (126.9322 35.12361) |
녹동 |N kdong | tation | OINT (126.934 35.10682) |
동구청 |Do g-gu Office | s ation | P INT (128.6322 35.8844) |
동대구 |Do gdaegu | s ation | P INT (128.6275 35.87742) |
북구청 |Bu -gu Office | s ation | P INT (128.5814 35.88381) |
평창 |P eongchang | tation | POINT (128.43 37.56196) |

The train stations are a collection of features

  • Just like before, the shapefile is a collection of features!
  • The only difference now is that each feature is a point

Reading and plotting shapefiles in R

Reading shapefiles in R

  • My go-to package for shapefiles in R is sf
  • Reading shapefiles is VERY easy! And you can treat them like dataframes.
Code 
library(sf)
# this is the shapefile for Gambia
gambia <- read_sf("vectorfilesdata/gambia.shp")
gambia
Simple feature collection with 115 features and 17 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: -16.81426 ymin: 13.04347 xmax: -13.79112 ymax: 13.82274
Geodetic CRS:  WGS 84
# A tibble: 115 × 18
   Shape_Leng Shape_Area ADM3_EN       ADM3_PCODE ADM3_REF ADM3ALT1EN ADM3ALT2EN
        <dbl>      <dbl> <chr>         <chr>      <chr>    <chr>      <chr>     
 1     0.0115 0.00000688 New Town East GM010101   <NA>     <NA>       <NA>      
 2     0.0206 0.0000161  New Town West GM010102   <NA>     <NA>       <NA>      
 3     0.0200 0.0000192  Soldier Town  GM010103   <NA>     <NA>       <NA>      
 4     0.0337 0.0000302  Box Bar       GM010201   <NA>     <NA>       <NA>      
 5     0.156  0.000591   Campama       GM010202   <NA>     <NA>       <NA>      
 6     0.0179 0.0000127  Crab Island   GM010203   <NA>     <NA>       <NA>      
 7     0.0322 0.0000533  Half Die      GM010301   <NA>     <NA>       <NA>      
 8     0.0216 0.0000236  Jollof Town   GM010302   <NA>     <NA>       <NA>      
 9     0.0203 0.0000257  Portugiese T… GM010303   <NA>     <NA>       <NA>      
10     0.494  0.00937    Basse         GM020101   <NA>     <NA>       <NA>      
# ℹ 105 more rows
# ℹ 11 more variables: ADM2_EN <chr>, ADM2_PCODE <chr>, ADM1_EN <chr>,
#   LGA_EN <chr>, ADM1_PCODE <chr>, ADM0_EN <chr>, ADM0_PCODE <chr>,
#   date <date>, validOn <date>, validTo <date>, geometry <POLYGON [°]>

Plotting is also very easy

Code 
ggplot() + 
  geom_sf(data = gambia)

My go-to theme

Code 
ggplot() +
  geom_sf(data = gambia) +
  theme_bw()

Other changes you can make

Code 
ggplot() +
  geom_sf(data = gambia, fill = "#D7D1CC", color = "#006334") +
  theme_bw() +
  labs(subtitle = "Admin3s in Gambia")

Give it a try with TAs (admin3) in Malawi (mw3.shp)

Code 
library(sf)
# this is the shapefile for the northern region of Malawi, TA level
northmw <- read_sf("vectorfilesdata/mw3.shp")
ggplot() +
  geom_sf(data = northmw)
Code 
ggplot() +
  geom_sf(data = northmw) +
  theme_bw() +
  labs(subtitle = "TAs in Northern Malawi")

One more example - map from earlier

Code 
admin2 <- read_sf("vectorfilesdata/mw2.shp")

ggplot() + 
  geom_sf(data = admin2, 
    fill = "white", color = kdisgray) +
  geom_sf(data = admin2 |> filter(DIST_CODE=="107"), 
    fill = "white", color = kdisgreen) +
  theme_bw() +
  labs(subtitle = "Districts in Northern Malawi")

What if we want to plot mw2, mw3, and mw4?

What if we want to plot mw2, mw3, and mw4?

Code 
admin2 <- read_sf("vectorfilesdata/mw2.shp")
admin3 <- read_sf("vectorfilesdata/mw3.shp")
admin4 <- read_sf("vectorfilesdata/mw4.shp")

g1 <- ggplot() + 
  geom_sf(data = admin2, fill = "white", color = "black") +
  theme_bw() + labs(subtitle = "A. Admin2 (districts)")
g2 <- ggplot() + 
  geom_sf(data = admin3, fill = "white", color = "black") +
  theme_bw() + labs(subtitle = "B. Admin3 (TAs)")
g3 <- ggplot() + 
  geom_sf(data = admin4, fill = "white", color = "black") +
  theme_bw() + labs(subtitle = "C. Admin4 (EAs)")

What if we want to plot mw2, mw3, and mw4?

  • Enter cowplot!
Code 
library(cowplot)

plot_grid(g1, g2, g3, ncol = 3)

A quick note about shapefile sizes

  • What do you think is the main determinant of the size of a shapefile?
  • The number of vertices!
    • Geographic size doesn’t really matter!
  • For the three Malawi shapefiles?
    • mw2.shp: 448 KB
    • mw3.shp: 4.9 MB
    • mw4.shp: 40.3 MB
  • And this is only for Northern Malawi.
    • The entire country is 123 MB
    • The 2023 shapefile from OSM for Indian roads is 236 MB
    • The shapefile of Indian villages is 614 MB

And that’s only shapefile

  • Other geospatial data can get even bigger!

  • How large do you think the folder on my computer that contains imagery for all of Malawi (at 5m resolution) is?

  • About 55 GB!

  • This is just a warning… I’ll generally always give you (relatively) small files for practice

Let’s talk about coordinates

Latitude and longitude on a globe

  • The most common coordinate reference system (CRS) is latitude/longitude
    • Latitude: North/South
    • Longitude: East/West
    • The equator is at 0° latitude
    • The prime meridian is at 0° longitude

  • But there’s a problem with using latitude/longitude
    • The Earth is a sphere (well, more or less; really an oblate spheroid)

The basic problem

  • The basic problem is that one degree of longitude changes at different latitudes!
    • At the equator, one degree of longitude is about 111 km
    • At 15N/S, one degree of longitude is about 107 km
    • At 30N/S, one degree of longitude is about 96 km
    • At 45N/S, one degree of longitude is about 79 km
    • At 60N/S, one degree of longitude is about 56 km
      • This explains Greenland!

  • It’s not an easy problem to solve, as all solutions have drawbacks!

Preserve shape, give up area

Projections

  • A projection is a way to represent the Earth’s surface on a flat plane
    • In other words, it’s a way to transform the three-dimensional surface of the earth into two dimensions
    • Think of this as a way to “flatten” the Earth
  • “Equal area” projections
    • These projections preserve the area of features
  • “Conformal” projections
    • These projections preserve the shape of features
  • It is impossible to perfectly preserve both!
    • But they can be close, especially in smaller areas
    • The earth looks quite flat from close up, after all

Robinson projection: compromise across the board

Meractor projection: preserves angular relationships

Azimuthal Equidistant projection

Mollweide Equal Area Cylindrical projection

Three families of projections

  • The QGIS website has a great explanation of the three families of projections
    • Cylindrical
    • Conical
    • Planar

Three families of projections

Coordinate reference systems

  • Coordinate reference systems (CRS) are a way to define how coordinates are represented
    • This includes the projection, but also other things
  • The most popular is probably WGS 84 (EPSG:4326), which is a geographic CRS
    • This is latitude/longitude
  • One degree of lat/lon:
    • 60 minutes
  • One minute:
    • 60 seconds
  • Geographic here means it is the location on the earth’s surface
    • This is different from a projected CRS, which is more about how to draw the earth on a flat surface

Geographic vs. projected

A common CRS: Universal Transverse Mercator (UTM)

  • Universal Transverse Mercator (UTM) is a projected CRS
    • It divides the world into 60 zones
    • Each zone is 6° wide
    • The equator is the origin of each zone
    • The equator is at 0 m

Universal Transverse Mercator (UTM)

A common CRS: Universal Transverse Mercator (UTM)

  • UTM defines X values (“longitude”) FROM THE MIDDLE of each zone

    • This middle line is called the central meridian

  • UTM defines Y values (“latitude”) from the equater

  • There are some other details:

    • UTM values are never negative, so we offset values
      • This is called a “false easting” and “false northing”
      • Details aren’t super important

  • Note: it ignores altitude. It assumes a perfect ellipsoid

“Transverse mercator” projection per zone (N and S)

Projections with sf

Code 
admin2 <- read_sf("vectorfilesdata/mw2.shp")

# Geographic CRS: WGS 84 - lat/lon
crs(admin2)
[1] "GEOGCRS[\"WGS 84\",\n    DATUM[\"World Geodetic System 1984\",\n        ELLIPSOID[\"WGS 84\",6378137,298.257223563,\n            LENGTHUNIT[\"metre\",1]]],\n    PRIMEM[\"Greenwich\",0,\n        ANGLEUNIT[\"degree\",0.0174532925199433]],\n    CS[ellipsoidal,2],\n        AXIS[\"geodetic latitude (Lat)\",north,\n            ORDER[1],\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n        AXIS[\"geodetic longitude (Lon)\",east,\n            ORDER[2],\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n    ID[\"EPSG\",4326]]"

What is the appropriate zone for Malawi?

  • Go to Google
    • Search “UTM CRS Malawi”
  • What did you find?
  • UTM zone 36S
  • With the sf package, we want to find the “EPSG” code to project
    • 20936

What is the appropriate zone for Malawi?

Code 
admin2proj <- st_transform(admin2, 20936)

# It has changed! Now it's projected
crs(admin2proj)
[1] "PROJCRS[\"Arc 1950 / UTM zone 36S\",\n    BASEGEOGCRS[\"Arc 1950\",\n        DATUM[\"Arc 1950\",\n            ELLIPSOID[\"Clarke 1880 (Arc)\",6378249.145,293.4663077,\n                LENGTHUNIT[\"metre\",1]]],\n        PRIMEM[\"Greenwich\",0,\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n        ID[\"EPSG\",4209]],\n    CONVERSION[\"UTM zone 36S\",\n        METHOD[\"Transverse Mercator\",\n            ID[\"EPSG\",9807]],\n        PARAMETER[\"Latitude of natural origin\",0,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8801]],\n        PARAMETER[\"Longitude of natural origin\",33,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8802]],\n        PARAMETER[\"Scale factor at natural origin\",0.9996,\n            SCALEUNIT[\"unity\",1],\n            ID[\"EPSG\",8805]],\n        PARAMETER[\"False easting\",500000,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8806]],\n        PARAMETER[\"False northing\",10000000,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8807]]],\n    CS[Cartesian,2],\n        AXIS[\"(E)\",east,\n            ORDER[1],\n            LENGTHUNIT[\"metre\",1]],\n        AXIS[\"(N)\",north,\n            ORDER[2],\n            LENGTHUNIT[\"metre\",1]],\n    USAGE[\n        SCOPE[\"Engineering survey, topographic mapping.\"],\n        AREA[\"Malawi. Zambia and Zimbabwe - east of 30°E.\"],\n        BBOX[-22.42,30,-8.19,35.93]],\n    ID[\"EPSG\",20936]]"

They look quite similar!

They look quite similar! Different coordinates

Code 
g1 <- ggplot(admin2) +
  geom_sf(fill = "white", color = kdisgreen) +
  theme_bw() +
  labs(subtitle = "A. Geographic CRS")
g2 <- ggplot(admin2proj) +
  geom_sf(fill = "white", color = kdisgreen) +
  theme_bw() +
  labs(subtitle = "B. Projected CRS") +
  coord_sf(crs = st_crs(20936))

Malawi is small. What about something larger?

Now it’s your turn!

  • Use the Indian roads shapefile (indiaprimaryroads.shp)

  • Do the following:

    • Find the CRS of the shapefile
    • Transform the shapefile to UTM zone 44N (EPSG: 24344)
    • Graph both side by side using cowplot

The solution

Code 
roads <- read_sf("vectorfilesdata/indiaprimaryroads.shp")
crs(roads)
[1] "GEOGCRS[\"WGS 84\",\n    DATUM[\"World Geodetic System 1984\",\n        ELLIPSOID[\"WGS 84\",6378137,298.257223563,\n            LENGTHUNIT[\"metre\",1]]],\n    PRIMEM[\"Greenwich\",0,\n        ANGLEUNIT[\"degree\",0.0174532925199433]],\n    CS[ellipsoidal,2],\n        AXIS[\"geodetic latitude (Lat)\",north,\n            ORDER[1],\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n        AXIS[\"geodetic longitude (Lon)\",east,\n            ORDER[2],\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n    ID[\"EPSG\",4326]]"
Code 
roadsproj <- st_transform(roads, 24344)
crs(roadsproj)
[1] "PROJCRS[\"Kalianpur 1975 / UTM zone 44N\",\n    BASEGEOGCRS[\"Kalianpur 1975\",\n        DATUM[\"Kalianpur 1975\",\n            ELLIPSOID[\"Everest 1830 (1975 Definition)\",6377299.151,300.8017255,\n                LENGTHUNIT[\"metre\",1]]],\n        PRIMEM[\"Greenwich\",0,\n            ANGLEUNIT[\"degree\",0.0174532925199433]],\n        ID[\"EPSG\",4146]],\n    CONVERSION[\"UTM zone 44N\",\n        METHOD[\"Transverse Mercator\",\n            ID[\"EPSG\",9807]],\n        PARAMETER[\"Latitude of natural origin\",0,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8801]],\n        PARAMETER[\"Longitude of natural origin\",81,\n            ANGLEUNIT[\"degree\",0.0174532925199433],\n            ID[\"EPSG\",8802]],\n        PARAMETER[\"Scale factor at natural origin\",0.9996,\n            SCALEUNIT[\"unity\",1],\n            ID[\"EPSG\",8805]],\n        PARAMETER[\"False easting\",500000,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8806]],\n        PARAMETER[\"False northing\",0,\n            LENGTHUNIT[\"metre\",1],\n            ID[\"EPSG\",8807]]],\n    CS[Cartesian,2],\n        AXIS[\"(E)\",east,\n            ORDER[1],\n            LENGTHUNIT[\"metre\",1]],\n        AXIS[\"(N)\",north,\n            ORDER[2],\n            LENGTHUNIT[\"metre\",1]],\n    USAGE[\n        SCOPE[\"Engineering survey, topographic mapping.\"],\n        AREA[\"India - onshore between 78°E and 84°E.\"],\n        BBOX[8.29,78,35.5,84.01]],\n    ID[\"EPSG\",24344]]"

The solution

Code 
g1 <- ggplot(roads) +
  geom_sf(fill = "white", color = kdisgreen) +
  theme_bw() +
  labs(subtitle = "A. Geographic CRS")
g2 <- ggplot(roadsproj) +
  geom_sf(fill = "white", color = kdisgreen) +
  theme_bw() +
  labs(subtitle = "B. Projected CRS") +
  coord_sf(crs = st_crs(24344))

plot_grid(g1, g2)

The solution

More practice

  • I’d like you to find a shapefile for a country of your choice
    • Ths isn’t always easy
    • I always use Google to find one
    • One place you can often find something on humdata.org (almost always shows up in the search!)
  • Do the following:
    • Find the CRS of the shapefile
    • Transform the shapefile to the appropriate UTM zone for the country
      • Note that many countries have multiple UTM zones! You can just choose one
    • Plot them side by side using cowplot

Returning to the files

  • Shapefiles are made up of at least four files:
    • .shp - the shape itself
      • The geometry
    • .shx - the index
      • The “index”. You can actual recover the .shx file from the .shp file
    • .dbf - the attributes
      • The attributes for each features. Could be names, population values, etc.
    • .prj - the projection
      • The projection information, which we just discussed
  • There are often more files, but these are the main ones
    • You must have the first three. The fourth is optional, but common.

Getting started with geospatial data, part II

  • What are we doing today?
    • Shapefiles
      • The packages terra and tidyterra
      • More practice on maps
  • Operations on shapefiles
    • Spatial merging
  • Areas and distances
  • More shapefile operations
    • Continued next week, too

The package terra

A new package

  • Last week, we used the sf package
    • This is a really nice, introductory way to ease into shapefiles
  • The terra package, though, is much more powerful
    • It is a complete replacement for the sf package
    • It is also a complete replacement for the raster package
    • It is also a complete replacement for the sp package
    • It is also a complete replacement for the rgdal package
    • Etc. etc. etc.

Loading a shapefile

Code 
library(terra)

# load the mw3 shapefile
mw3 <- vect("vectorfilesdata/mw3.shp")

mw3
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 76, 2  (geometries, attributes)
 extent      : 493675.9, 691460, 8591761, 8964834  (xmin, xmax, ymin, ymax)
 source      : mw3.shp
 coord. ref. : Arc 1950 / UTM zone 36S 
 names       : TA_CODE DIST_CODE
 type        :   <chr>     <chr>
 values      :   10120       101
                 10110       101
                 10102       101

Saving a shapefile

Code 
# with terra
writeVector(mw3, "locationoffile.shp")
# with sf
write_sf(mw3, "locationoffile.shp")

Plotting the shapefile

Code 
# terra uses base R plots by default!
plot(mw3)

I don’t use base R… so ggplot!

Code 
# we need this library to use ggplot with terra objects
library(tidyterra)
ggplot() + 
  geom_spatvector(data = mw3) +
  theme_bw()

Find the name of the district variable

Find the name of the district variable

Code 
ggplot() + 
  geom_spatvector(data = mw3, aes(fill = DIST_CODE)) +
  theme_bw()

Note that you can extract variables with $

Code 
mw3$DIST_CODE
 [1] "101" "101" "101" "101" "101" "101" "101" "101" "101" "101" "101" "102"
[13] "102" "102" "102" "102" "102" "102" "106" "106" "105" "105" "105" "105"
[25] "105" "105" "105" "105" "105" "105" "105" "105" "105" "107" "107" "107"
[37] "107" "107" "107" "107" "107" "107" "107" "107" "107" "107" "107" "107"
[49] "103" "103" "103" "103" "103" "103" "103" "103" "103" "103" "103" "103"
[61] "103" "103" "104" "104" "104" "104" "104" "104" "104" "104" "104" "104"
[73] "104" "104" "104" "104"

What if we want to aggregate to districts?

  • i.e. we want to “aggregate” or “dissolve” polygons

What if we want to create a new shapefile with districts?

Code 
mw2 <- aggregate(mw3, by = "DIST_CODE")
nrow(mw2)
[1] 7
Code 
# check if mw3 has same number of districts
length(unique(mw3$DIST_CODE))
[1] 7

What if we want to create a new shapefile with districts?

What if we want to create a new shapefile with districts?

What if we want to do something like this?

Let’s start simpler!

A bunch of steps!

  1. Load the shapefile
  1. Create bounding boxes and convert to vect
  1. Intersect the shapefile with the bounding boxes

  1. Plot the shapefile with the bounding boxes

    • This last one takes a lot of experimentation

Step 1: Load the shapefile

  • Please download the mw3allcountry.zip file and extract to your computer
    • Then load it using vect()



Code 
mw3all <- vect("vectorfilesdata/mw3allcountry.shp")
# we'll use this variable
mw3all$surveyobs
   [1]   0   0   0   0  16   0  16  16  16   0  16   0   0   0   0   0   0   0
  [19]   0  16   0   0   0  16   0   0   0   0   0   0   0  16   0   0   0   0
  [37]  16  16   0   0   0   0   0   0   0  16   0   0  16   0   0  16   0   0
  [55]   0   0  32   0   0   0   0  16   0  16   0   0   0   0  16   0   0   0
  [73]   0   0   0   0   0  16   0   0   0   0  16   0   0   0   0   0   0  16
  [91]   0   0  16 369  16   0   0   0   0   0   0   0  16  16   0   0   0   0
 [109]   0   0   0   0  16   0   0   0   0  16   0  16   0   0   0   0   0   0
 [127]   0   0   0   0  15   0   0  16   0   0   0   0   0   0  16   0   0  16
 [145]  16   0   0   0   0   0  16   0   0   0   0  16   0   0   0   0  16   0
 [163]   0   0   0  16   0   0   0   0  16   0   0   0   0   0  16   0   0   0
 [181]   0   0   0  16   0   0   0   0   0   0   0   0  32   0   0   0   0   0
 [199]  16   0   0   0   0   0   0  16  16   0   0   0   0   0   0   0   0   0
 [217]   0   0   0   0  16   0   0   0   0  16   0   0  16   0   0  16   0   0
 [235]   0   0  16   0   0   0   0   0   0  16   0   0   0  16   0   0   0   0
 [253]  16  16   0   0   0   0   0   0   0   0   0  16   0   0   0   0  16   0
 [271]  16   0   0   0   0   0   0   0   0  16   0   0   0   0   0   0   0   0
 [289]  16   0   0   0   0   0  16  16   0   0   0  16   0   0  32   0   0   0
 [307]   0   0   0   0   0   0   0   0   0   0   0   0  16   0   0   0   0   0
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 [343]   0   0  16  31   0   0   0  16   0   0   0   0  16   0   0   0   0   0
 [361]   0   0   0  32   0   0  16  16   0   0   0   0   0   0   0   0  16  16
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 [397]   0   0   0  16   0   0   0   0  32   0   0   0  16   0   0  16  32   0
 [415]   0   0  16  16  16   0  16  16  16  16  16   0  16  16  16  16  16   0
 [433]  16   0   0   0  16   0   0   0   0  16   0   0  32   0   0   0  16  16
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[1351]   0   0   0   0   0  16   0   0   0   0   0   0  16   0   0   0  16   0
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[1567]   0   0   0  16   0   0   0   0   0   0   0   0   0   0   0   0   0  14
[1585]   0   0   0   0   0   0   0   0   0  32   0   0   0   0   0   0   0   0
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[1855]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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[1927]   0   0   0   0  16   0   0  16   0   0   0   0   0   0  16  16   0   0
[1945]   0   0   0   0   0  16  16   0   0   0   0   0   0   0   0  16  16   0
[1963]  16   0   0  16  32  16  16  16   0  16  32   0  16  15  16  16   0   0
[1981]  16  32   0   0   0   0 336  16   0   0   0   0   0   0   0   0   0   0
[1999]   0   0   0   0   0   0   0  16   0   0  16   0   0   0   0   0   0   0
[2017]   0   0   0   0   0  16   0  16   0   0   0   0   0   0   0   0   0   0
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[2269]  16   0   0   0   0   0  16   0   0  16  16  16   0  15  16   0   0  16
[2287]   0   0   0   0  16   0   0   0   0  32   0   0  16   0   0   0  16   0
[2305]   0  16  16   0   0   0   0  16  32   0   0   0   0   0  16  16   0   0
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[2377]   0   0   0   0   0   0   0   0   0   0   0   0   0  16   0   0   0   0
[2395]   0  16   0   0   0   0   0   0   0   0   0   0   0  16   0   0   0  16
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[2503]  16  16  16  16   0   0   0  16   0   0   0   0   0   0   0  32   0  16
[2521]  16  16   0  16  16   0  16   0  16   0   0  16   0   0   0   0   0   0
[2539]  16  16   0   0   0  16   0   0  16   0   0   0   0   0  16   0   0   0
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[2611]   0   0   0   0   0  16   0   0   0   0   0   0  16  16   0  16   0   0
[2629]   0   0  16   0   0   0  16   0  16   0  16  16  16  28   0   0   0   0
[2647]   0   0  16   0   0   0  32   0  16   0   0  16  16   0   0   0  16  16
[2665]   0  16   0   0  16   0  16   0   0  16  48   0   0   0  16   0   0   0
[2683]  16  16   0   0   0   0   0   0   0   0  32   0   0   0  16   0   0   0
[2701]   0  16   0   0  16   0   0  16   0   0  16   0   0   0   0   0   0  16
[2719]   0   0   0  16   0   0   0   0  16   0   0  16   0   0   0   0   0   0
[2737]  16  16   0  16   0   0  16   0   0   0   0   0  16   0   0   0   0  16
[2755]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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[2791]  16   0   0  16   0   0   0   0   0   0   0   0   0  16   0   0   0   0
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[2827]   0   0   0   0  16   0   0  16   0   0   0  16   0   0   0   0   0   0
[2845]   0   0  16   0   0  16   0   0   0   0  16   0   0   0   0   0   0   0
[2863]   0   0   0  16   0   0   0   0   0  16   0   0   0   0   0   0   0  16
[2881]   0   0   0   0   0  16   0   0   0   0   0   0   0  16   0   0   0   0
[2899]  16   0   0   0   0   0  16   0   0   0   0   0   0   0   0   0  16   0
[2917]   0   0   0   0   0   0   0   0   0  16   0   0   0   0   0   0   0   0
[2935]   0  16   0   0   0   0   0   0  16   0   0  16   0   0   0   0   0   0
[2953]  16   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
[2971]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  32   0
[2989]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  16
[3007]   0   0   0   0  16   0   0   0   0   0   0   0   0  16  16   0   0   0
[3025]   0  16   0   0  16   0   0   0   0   0   0   0   0   0   0   0   0  16
[3043]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  16   0
[3061]   0   0   0   0   0   0   0  16   0   0  16  16   0   0   0   0   0   0
[3079]   0   0  16   0   0   0   0   0   0   0   0   0   0  16   0   0  16   0
[3097]   0   0   0   0   0   0   0   0   0   0  16   0   0   0   0   0   0  16
[3115]   0   0   0   0   0  16   0   0   0   0   0 316

Step 2: Create bounding boxes (extent)

  • Now we have to find the extent of Lilongwe and Blantyre
    • Look through the data
    • What variables might help us with this?
Code 
mw3all
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 3126, 16  (geometries, attributes)
 extent      : 32.67152, 35.91505, -17.12721, -9.363796  (xmin, xmax, ymin, ymax)
 source      : mw3allcountry.shp
 coord. ref. : lon/lat WGS 84 (EPSG:4326) 
 names       :  ID_0   ISO NAME_0  ID_1 NAME_1  ID_2      NAME_2  ID_3
 type        : <num> <chr>  <chr> <num>  <chr> <num>       <chr> <num>
 values      :   135   MWI Malawi     1 Balaka     1 Balaka Town     1
                 135   MWI Malawi     1 Balaka     1 Balaka Town     2
                 135   MWI Malawi     1 Balaka     1 Balaka Town     3
      NAME_3 CCN_3 (and 6 more)
       <chr> <num>             
 n.a. (1951)     0             
 n.a. (1953)     0             
 n.a. (1954)     0

Step 2: Create bounding boxes (extent)

  • Let’s look at the NAME_1 variable
Code 
unique(mw3all$NAME_1)
 [1] "Balaka"     "Blantyre"   "Chikwawa"   "Chiradzulu" "Chitipa"   
 [6] "Dedza"      "Dowa"       "Karonga"    "Kasungu"    "Likoma"    
[11] "Lilongwe"   "Machinga"   "Mangochi"   "Mchinji"    "Mulanje"   
[16] "Mwanza"     "Mzimba"     "Neno"       "Nkhata Bay" "Nkhotakota"
[21] "Nsanje"     "Ntcheu"     "Ntchisi"    "Phalombe"   "Rumphi"    
[26] "Salima"     "Thyolo"     "Zomba"

Step 2: Create bounding boxes (extent)

  • Let’s create new shapefiles for Lilongwe and Blantyre
    • How?
Code 
lilongwe <- mw3all[mw3all$NAME_1=="Lilongwe",]
blantyre <- mw3all[mw3all$NAME_1=="Blantyre",]
  • Now create extents
Code 
lilongwebox <- ext(lilongwe)
blantyrebox <- ext(blantyre)

Step 2: Create bounding boxes (extent)

  • What is an extent?
    • We’ve covered this before!
Code 
lilongwebox
SpatExtent : 33.2449913024903, 34.2784042358398, -14.6049509048462, -13.4817895889282 (xmin, xmax, ymin, ymax)


Code 
blantyrebox
SpatExtent : 34.7182960510255, 35.1323623657227, -16.0146331787109, -15.3487529754639 (xmin, xmax, ymin, ymax)

Step 2: Create bounding boxes (extent)

  • You can actually plot those as is!
    • But let’s explicitly give them the correct CRS (and turn them into vect objects)
Code 
lilongwebox <- vect(lilongwebox, crs = crs(mw3all))
  • Try it for Blantyre
Code 
blantyrebox <- vect(blantyrebox, crs = crs(mw3all))

Let’s plot them with the original shapefile

Code 
ggplot() + 
  geom_spatvector(data = mw3all, 
    aes(fill = surveyobs), color = NA) +
  geom_spatvector(data = lilongwebox, 
    fill = NA, color = "black") +
  geom_spatvector(data = blantyrebox, 
    fill = NA, color = "black") +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw()

Step 3: Intersect the shapefile with the bounding boxes

  • Now we need to intersect the shapefile with the bounding boxes
    • This will give us the shapefiles for Lilongwe and Blantyre
Code 
lilongwe <- intersect(mw3all, lilongwebox)
ggplot() + 
  geom_spatvector(data = lilongwe, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw()

Go ahead and do the same for Blantyre

(and plot it!)

Go ahead and do the same for Blantyre

Code 
blantyre <- intersect(mw3all, blantyrebox)
ggplot() + 
  geom_spatvector(data = blantyre, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw()
  • Note the legend scale changed!
    • We’ll correct that later

Step 4. Plot the shapefile with the bounding boxes

  • This is the hard part!
    • A couple hard things:
  • Grid size:
    • For Malawi, the grid is quite small
    • We want to expand it a bit
  • Finding the right locations:
    • It takes experimentation to figure out where to put the insets

Expanding the grid - can you spot the difference?

We do this with expand_limits

  • If we provide expand_limits with a single x coordinate, it will expand the grid to include that coordinate
  • What does this code do?


Code 
ggplot() + 
  geom_spatvector(data = mw3all, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  theme(legend.position = "bottom") +
  expand_limits(x = ext(mw3all)[2] + 2.5)

Adding insets

  • We can use cowplot to add insets to our plot
    • This is a bit tricky, but it’s a nice way to show multiple levels of detail
  • Step 1:
    • Create main plot and save (I’ll save as g1)
  • Step 2:
    • Create the insets and save them
    • I’ll save them as g2 and g3
  • Step 3:
    • Use ggdraw to add insets

Step 1: Create the main plot

Code 
g1 <- ggplot() + 
  geom_spatvector(data = mw3all, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  theme(legend.position = "bottom") +
  expand_limits(x = ext(mw3all)[2] + 2.5)

Step 1: Create the main plot

Step 2: Create the insets

Code 
g2 <- ggplot() + 
  geom_spatvector(data = lilongwe, 
    aes(fill = surveyobs), color = NA,
    show.legend = FALSE) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  # this part is important!
  theme(plot.background = element_rect(fill = "transparent", color = "transparent")) +
  theme(axis.title.x = element_blank(),
        axis.text.x=element_blank(),
        axis.ticks.x=element_blank()) +
  theme(axis.title.y=element_blank(),
        axis.text.y=element_blank(),
        axis.ticks.y=element_blank())

Step 2: Create the insets

Step 2: Create the insets

  • Go ahead and do it for Blantyre
Code 
g3 <- ggplot() + 
  geom_spatvector(data = blantyre, 
    aes(fill = surveyobs), color = NA,
    show.legend = FALSE) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  theme(axis.title.x = element_blank(),
        axis.text.x=element_blank(),
        axis.ticks.x=element_blank()) +
  theme(axis.title.y=element_blank(),
        axis.text.y=element_blank(),
        axis.ticks.y=element_blank()) +
  theme(plot.background = element_rect(fill = "transparent", color = "transparent"))

Step 2: Create the insets

Step 3: Add insets with ggdraw

Code 
ggdraw(g1) +
  draw_plot(g2 + theme(legend.position = "none"), 
    x = ??, y = ??, height = ??, width = ??) +
  draw_plot(g3 + theme(legend.position = "none"), 
    x = ??, y = ??, height = ??, width = ??)
  • This is where the experimentation comes in!
    • All the ?? values need to be between 0 and 1
    • They represent proportions of the plot
    • The legend.position = "none" is just to make sure it’s not there!
  • Give it a try. See if you can come up with a good combination!
    • I’ll show you what I did in a minute

Step 3: Add insets with ggdraw

Code 
ggdraw(g1) +
  draw_plot(g2, x = 0.425, y = 0.6, height = 0.275, width = 0.275) +
  draw_plot(g3, x = 0.485, y = 0.23, height = 0.275, width = 0.2) +

Step 3: Add insets with ggdraw

This still isn’t quite right

  • There are still some changes to make
    • Can you spot them?
  • The legend for Blantyre is wrong!
  • Let’s delete the “x” axis label
  • Let’s put the legend title on top
  • Add subtitles for Blantyre and Lilongwe

The Blantyre legend - what’s the difference?

Using limits in scale_fill_distiller

Code 
g3 <- ggplot() + 
  geom_spatvector(data = blantyre, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral", 
    limits = c(min(mw3all$surveyobs), max(mw3all$surveyobs))) +
  theme_bw()
  • This also works with all the other scale_ options
    • scale_fill_brewer, scale_color_brewer, etc.

Delete the x-axis label

Delete the x-axis label

  • See if you can find an answer on Google!
    • There are a couple possible ways to do it
Code 
g1 <- ggplot() + 
  geom_spatvector(data = mw3all, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  theme(legend.position = "bottom") +
  expand_limits(x = ext(mw3all)[2] + 2.5) +
  theme(axis.title.x = element_blank())

Finally, move legend title to top

Finally, move legend title to top

Code 
g1 <- ggplot() + 
  geom_spatvector(data = mw3all, 
    aes(fill = surveyobs), color = NA) +
  scale_fill_distiller("Survey\nobservations", 
    palette = "Spectral") +
  theme_bw() +
  theme(legend.position = "bottom") +
  expand_limits(x = ext(mw3all)[2] + 2.5) +
  theme(axis.title.x = element_blank()) +
  guides(fill = guide_colorbar(title.position="top", title.hjust = 0.5))
  • Note that if it’s a color instead of a fill, should be color = instead of fill =

Adding titles for the insets

  • How do you add a title to Blantyre and Lilongwe?
    • Note that I use subtitle here because it’s a bit smaller (you could also change the text size)

labs(subtitle = "Lilongwe")

labs(subtitle = "Blantyre")

One more small change: the width of the legend

theme(legend.key.width = unit(0.5, "inches"))

Putting it all together

Intersections and spatial joins

Let’s move on to a new topic

  • Here’s our goal:
    • We want to count the number of points in each polygon
    • We want to count points in each ADMIN2 (not admin3)
  • We have two files: one is data with lon/lat coordinates and one is admin3 polygons
    • We need to create a shapefile from the points
    • We need to aggregate the admin3 to admin2
    • We need to extract the admin2 identifier into points
    • Then we need to join the two together

What we need

  • Points: points.csv
    • This is a list of health facilities in Malawi
    • Note that this data is NOT complete (it comes from OpenStreetMap)
  • Polygons: mw3allcountry.shp
    • Let’s use the entire country

Step 1: Load the points

Code 
# note that this function is in tidyverse!
points <- read_csv("vectorfilesdata/points.csv")
  • Find the name of the columns that represent the coordinates
    • We’ll need these to create the spatial object
Code 
# Let's turn it into a `terra` object
points <- vect(points, geom = c("x", "y"), crs = "EPSG:4326") # these are lon/lat
points
 class       : SpatVector 
 geometry    : points 
 dimensions  : 155, 1  (geometries, attributes)
 extent      : 32.88771, 35.71544, -16.52659, -9.496221  (xmin, xmax, ymin, ymax)
 coord. ref. : lon/lat WGS 84 (EPSG:4326) 
 names       :          fclass
 type        :           <chr>
 values      : health facility
               health facility
               health facility

Let’s just plot the points

Code 
ggplot() + 
  geom_spatvector(data = points) +
  theme_bw()

Now let’s load the admin3 and aggregate

Code 
adm3 <- vect("vectorfilesdata/mw3allcountry.shp")
  • Do you remember how to aggregate to admin2?
    • You need to use aggregate and the column name!
    • Look at the column names
Code 
adm2 <- aggregate(adm3, "ID_2")

Let’s plot it

Code 
ggplot() + 
  geom_spatvector(data = adm2) +
  theme_bw()

Time to extract

  • We are going to use the function relate to find which adm2 feature the point lies within
    • This is a spatial join
    • We are also going to use this to learn a bit more about R
Code 
# let's first make sure it's the same CRS!
points <- project(points, crs(adm2))

join <- relate(adm2, points, "contains")
# check the dimensions
dim(join)
[1] 256 155

The apply function

Example data
col1 col2 col3 col4
Point 1 TRUE FALSE FALSE TRUE
Point 2 FALSE FALSE TRUE FALSE
Point 3 FALSE TRUE FALSE TRUE
Point 4 FALSE TRUE TRUE FALSE
Point 5 FALSE FALSE FALSE TRUE
Point 6 TRUE TRUE FALSE TRUE


  • Let’s look at an example
  • An important note:
    • If you take the mean of logical statements, it treats TRUE as 1 and FALSE as 0
    • Same with sum

The apply function

Example data
col1 col2 col3 col4
Point 1 TRUE FALSE FALSE TRUE
Point 2 FALSE FALSE TRUE FALSE
Point 3 FALSE TRUE FALSE TRUE
Point 4 FALSE TRUE TRUE FALSE
Point 5 FALSE FALSE FALSE TRUE
Point 6 TRUE TRUE FALSE TRUE


  • In this data, what happens if we:
    • Take the sum of each row?
    • What values do we get?

The apply function

Example data
col1 col2 col3 col4 sum
Point 1 TRUE FALSE FALSE TRUE 2
Point 2 FALSE FALSE TRUE FALSE 1
Point 3 FALSE TRUE FALSE TRUE 2
Point 4 FALSE TRUE TRUE FALSE 2
Point 5 FALSE FALSE FALSE TRUE 1
Point 6 TRUE TRUE FALSE TRUE 3
  • We can use the apply function to do this!
    • data$sum = apply(data, 1, "sum")
    • This will sum each row and put it in a new column called sum
    • What happens if we instead use "mean"?
  • The 1 denotes doing this by row… how do we apply the function by column?

The apply function

Example data
col1 col2 col3 col4 mean
Point 1 TRUE FALSE FALSE TRUE 0.5
Point 2 FALSE FALSE TRUE FALSE 0.25
Point 3 FALSE TRUE FALSE TRUE 0.5
Point 4 FALSE TRUE TRUE FALSE 0.5
Point 5 FALSE FALSE FALSE TRUE 0.25
Point 6 TRUE TRUE FALSE TRUE 0.75


data$mean = apply(data, 1, "mean")

Back to our data

  • Check the dimensions of the data
    • What do rows and what do columns represent?
Code 
dim(join)
[1] 256 155
Code 
join
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[205,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[206,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[207,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[208,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[210,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[214,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[219,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[222,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[225,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[238,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[239,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[240,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[241,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[242,] FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
[243,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[244,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[245,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[246,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[247,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[248,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[249,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[250,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[252,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[253,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
       [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
  [3,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[145,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
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[211,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[212,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[214,] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[216,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[217,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[223,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[224,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[225,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[226,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[229,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[230,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[231,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
[232,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[235,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[244,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[245,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[246,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[248,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[250,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[253,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
       [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60]
  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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  [4,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
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 [82,] FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
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[108,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[109,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
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[111,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[131,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[135,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[136,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[137,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[155,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[157,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[186,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[187,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
[188,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[189,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[190,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[191,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[192,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[195,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[199,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[200,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[201,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[202,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[203,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[204,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[205,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[206,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[207,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[208,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[209,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[210,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[211,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[212,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[213,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[214,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[215,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[216,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[217,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[218,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[219,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[221,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[222,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[223,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[224,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
[225,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[226,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[227,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[228,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[229,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[230,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[231,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[232,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[233,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[234,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[235,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[236,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[237,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[238,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[239,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[240,] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
[241,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[242,] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[243,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[244,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[245,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[246,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[247,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[248,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[249,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[250,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[251,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[252,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[253,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
       [,61] [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72]
  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [3,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE
  [4,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[148,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[149,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[150,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
[151,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[152,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[153,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[154,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[155,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[159,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[160,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[170,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[192,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[194,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
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[201,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[202,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[203,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
[204,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[205,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[206,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[207,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[208,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[209,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[210,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[211,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[212,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[213,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[214,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[215,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[216,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[217,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[218,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[219,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[221,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[222,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[223,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[224,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[225,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[226,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[227,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[228,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[229,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[230,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[231,] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[232,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[233,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[234,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[235,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[236,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[237,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[238,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[239,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[240,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[241,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[242,] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE
[243,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[244,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[245,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[246,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[247,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[248,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[249,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[250,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[251,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[252,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[253,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
       [,73] [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84]
  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [3,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
  [4,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
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 [35,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
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[153,] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[160,] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
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[191,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[192,] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[210,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
       [,85] [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96]
  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[141,] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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[202,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[203,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[204,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[205,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[206,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[207,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[208,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[209,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[210,] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[211,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[212,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[213,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[214,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[215,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[216,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[217,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[218,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
[219,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[220,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[221,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[222,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[223,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[224,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[225,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[226,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[227,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[228,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[229,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[230,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[231,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[232,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[233,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[234,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[235,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[236,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[237,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[238,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[239,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[240,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[241,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[242,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
[243,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[244,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[245,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[246,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[247,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[248,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[249,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[250,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[251,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[252,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[253,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[254,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[255,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[256,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
       [,97] [,98] [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106]
  [1,] FALSE FALSE FALSE   TRUE  FALSE  FALSE  FALSE  FALSE  FALSE  FALSE
  [2,] FALSE FALSE FALSE  FALSE  FALSE  FALSE  FALSE  FALSE  FALSE  FALSE
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       [,117] [,118] [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126]
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How do we use apply here?

  • So the columns are POINTS and the rows are POLYGONS (adm2)
  • What do we want to do?
  • We want to find the number of points in each polygon
    • It is TRUE/FALSE so we want to sum BY rows!

How do we use apply here?

Code 
adm2$points = apply(join, 1, "sum")
adm2$points
  [1]  2  2  2 14  0  1  0  0  0  1  0  0  0  0  0  1  1  0  1  2  0  0  0  0  0
 [26]  0  0  0  0  0  1  0  0  0  4  0  0  1  0  0  0  0  1  0  1  0  0  0  1  0
 [51]  0  1  0  0  0  0  1  2  0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0
 [76]  0  0  0  0  0  0 22  1  2  0  0  2  2  3  0  1  2  0  0  1  1  1  0  0  0
[101]  1  0  0  0  0  0  0  0  2  0  0  0  0  1  1  0  0  0  0  0  0  0  1  3  1
[126]  0  0  0  0  0  1  1  0  1  1  0  1  0  0  0  1  0  0  3  7  0  0  0  0  1
[151]  1  0  1  0  0  0  0  3  0  1  2  1  0  0  0  0  1  0  0  0  0  0  1  0  0
[176]  0  0  1  0  0  0  0  0  0  0  0  3  0  0  0  0  1  0  1  0  0  0  0  0  0
[201]  0  0  1  0  0  0  0  0  0  1  0  0  0  1  0  0  0  1  0  0  0  0  0  1  1
[226]  1  0  0  0  1  2  0  0  0  0  0  0  0  0  2  0  6  1  0  0  0  1  0  0  0
[251]  0  0  0  0  1  7

Now we can graph it!

Code 
ggplot() + 
  geom_spatvector(data = adm2, aes(fill = points)) +
  scale_fill_distiller("Number of\npoints", palette = "Spectral") +
  theme_bw()

Make it a little nicer

Code 
ggplot() + 
  geom_spatvector(data = adm2, aes(fill = points), color = NA) +
  scale_fill_distiller("Number of\npoints", palette = "Spectral") +
  theme_bw()

Now it’s your turn!

  • I have uploaded a map of Korea
    • It is at the shi/gun/gu (시군구) level
    • It is called kcities.shp (also a .zip there)
  • I have also uploaded a list of points
    • These are train stations
    • It is called krail.csv
  • Your task: Find how many train stations there are in each feature!
    • Then map it
  • I’ll give you 10-15 minutes
    • Then I’ll open a script and we’ll do it together

Calculating areas and lengths

  • We can also calculate areas and lengths!

  • perim for length

    • For polygons, it returns the length of the perimeter
    • For lines, it returns the length of the line

  • expanse for area

    • Returns the area of polygons
    • What will it return for lines or points?

  • Believe it or not, using lon/lat gives the most accurate results!

Area

  • Let’s use the adm3 shapefile
Code 
adm3$area <- expanse(adm3, unit="km", transform = TRUE)
  • Unit: do you want \(km^2\) or \(m^2\)?
  • Transform: automatically transform to lon/lat?
    • Always do this. terra documentation says this will be more accurate

Area

Perimeter

Code 
adm3$perimeter <- perim(adm3 |> project("EPSG:4326"))


  • This automatically gives length in meters
  • You can add project with a pipe operator |> to transform to lon/lat

Perimeter

More distances

  • We have points for households

  • We have points for health facilities

  • We can calculate the distance between each household and each health facility

    • Finding distances between points is a common GIS task!

Distance matrix

  • The name of the households data is households.dta
    • This is a Stata dataset
    • You can read it using the package haven
  • Please go ahead and try loading the dataset and then turning it into a terra object
    • You’ll have to find the names of the columns that represent the coordinates

Distance matrix

Code 
# households
households <- read_dta("vectorfilesdata/households.dta")
households <- vect(households, geom = c("ea_lon_mod", "ea_lat_mod"), crs = "EPSG:4326")
# health facilities
# do it in one line!
health <- vect(read_csv("vectorfilesdata/points.csv"), geom = c("x", "y"), crs = "EPSG:4326")

Distance matrix

Code 
distances <- distance(households, health)
dim(households)
[1] 11290    42
Code 
dim(health)
[1] 155   1
Code 
dim(distances)
[1] 11290   155

Distance matrix - “Heat map”

Closest health facility by household

How did I create the map?

  • The distances object is a matrix
    • What are the rows and what are the columns?
  • If we want to find the closest health facility to each household, what do we need to do?
    • We need to find the minimum distance for each row
    • Do you remember?

Closest health facility by household

  • We can use the apply function!
    • But with "min" instead of "sum"
    • The rows are in the same order as the households, so…
Code 
distances <- distance(households, health)
closest <- apply(distances, 1, "min")

# they're in the same order!
households$closest <- closest

ggplot() + 
  geom_spatvector(data = households, aes(color = closest/1000), size = 0.5) +
  scale_color_distiller("Distances\n(km)", palette = "Spectral") +
  theme_bw()

More advanced operations

Let’s go over some more advanced operations

  • This stuff will spillover into next week

  • First up:

    • Spatial overlap

A grid in Korea - kgrid.zip

A grid in Korea - kgrid.zip

  • We will discuss how to make a grid after we learn about rasters

  • For now, the grid is a shapefile

  • A very common operation:

    • We want to know which province/city each grid cell is in
    • This isn’t straightforward. Why?
  • A grid cell can overlap multiple provinces/cities

The data

  • Here is the data:
    • kshape.shp is the shapefile of the provinces/cities
    • kgrid.shp is the grid
    • I have uploaded .zip files for both


Code 
kshape <- vect("vectorfilesdata/kshape.shp")
kgrid <- vect("vectorfilesdata/kgrid.shp")
kgrid
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 4906, 1  (geometries, attributes)
 extent      : 746110.3, 1306110, 1458754, 2068754  (xmin, xmax, ymin, ymax)
 source      : kgrid.shp
 coord. ref. : KGD2002_Unified_Coordinate_System (ESRI:102080) 
 names       :    id
 type        : <num>
 values      :    65
                  66
                  67

The intersect function from terra

  • We are going to use the intersect function

  • Here’s what it will do:

    • It will find the intersection of the grid cell and the province/city
    • Except, it will return a new feature for EACH overlap

  • Let’s look at some maps

The intersect function from terra

The intersect function from terra

Code 
intersection <- intersect(kgrid, kshape)
intersection
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 5546, 3  (geometries, attributes)
 extent      : 746110.3, 1304099, 1458754, 2068444  (xmin, xmax, ymin, ymax)
 coord. ref. : KGD2002_Unified_Coordinate_System (ESRI:102080) 
 names       :    id CTPRVN_CD CTP_ENG_NM
 type        : <num>     <chr>      <chr>
 values      :    65        51 Gangwon-do
                  66        51 Gangwon-do
                  67        51 Gangwon-do
Code 
kgrid
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 4906, 1  (geometries, attributes)
 extent      : 746110.3, 1306110, 1458754, 2068754  (xmin, xmax, ymin, ymax)
 source      : kgrid.shp
 coord. ref. : KGD2002_Unified_Coordinate_System (ESRI:102080) 
 names       :    id
 type        : <num>
 values      :    65
                  66
                  67

One grid cell, multiple overlaps

One grid cell, multiple overlaps

Area of overlap

  • So what do we want to do?
    • Let’s find the area of overlap for each grid cell and each province/city
    • Then let’s take the LARGEST overlap and assign that to the grid cell
    • In practice, depending on the context, you could use a weighted mean or something else
      • This won’t work with categorical variables, though
Code 
# Get area of all overlaps
intersection$area <- expanse(intersection)
# turn it into a tibble
intersection <- as_tibble(intersection)
# Get the largest overlap
intersection <- intersection |> group_by(id) |> filter(area==max(area)) |> ungroup()

Area of overlap

Code 
intersection
# A tibble: 4,906 × 4
      id CTPRVN_CD CTP_ENG_NM      area
   <dbl> <chr>     <chr>          <dbl>
 1    65 51        Gangwon-do   332498.
 2    66 51        Gangwon-do  3885964.
 3    67 51        Gangwon-do  1659454.
 4   193 51        Gangwon-do   477650.
 5   194 51        Gangwon-do 12783973.
 6   195 51        Gangwon-do 14674738.
 7   321 51        Gangwon-do   289674.
 8   322 51        Gangwon-do 14274204.
 9   323 51        Gangwon-do 22582297.
10   324 51        Gangwon-do   604121.
# ℹ 4,896 more rows
Code 
kgrid
 class       : SpatVector 
 geometry    : polygons 
 dimensions  : 4906, 1  (geometries, attributes)
 extent      : 746110.3, 1306110, 1458754, 2068754  (xmin, xmax, ymin, ymax)
 source      : kgrid.shp
 coord. ref. : KGD2002_Unified_Coordinate_System (ESRI:102080) 
 names       :    id
 type        : <num>
 values      :    65
                  66
                  67